In this paper, an improved flat triangular shell element is proposed. This element has three nodes, and in each node, six degrees of freedom are considered. Since there are three rotational degrees of freedom at each node, the drilling effect can be incorporated in authors' formulation. A new procedure is also suggested for updating the director vectors about which the rotational degrees of freedom are defined. In order to study large displacements and rotations, Total Lagrangian principles are employed. In addition, updating the rotational degrees of freedom is implemented using enriched updated director vectors, which are formulated based on the finite rotation method. On the other hand, small strains are considered in this formulation. By utilizing MITC method, shear and membrane locking is mitigated from new element. To examine the performance, the element passes three basic tests, including isotropy, and patch test. Moreover, a convergence study is also implemented to show the elemental behavior. Several popular benchmarks are considered to illustrate the accuracy and capability of the suggested element in geometrically nonlinear analyses.
Efficient three-node finite shell element for linear and geometrically nonlinear analyses of piezoelectric laminated structures
